Statisitcs Practical 21-24/5/2019
Gordon McLachlan
24 May 2019
Getting Lost In Statistics
Some journeys are longer than others.
Workflow Steps;
1. Create Git Repository
2. Import & Tidy Data
3. Visualise Data, ggplot
4. Statisical Model
5. Markdown Document
Work will be stored on laptop & github, in the directory structure below;
StatsPrac190521
-Data (data will remain on laptop, not on github)
-Scripts (laptop & github)
-Results (laptop & github)
MulligansFlatInfiltration
Water infiltration measurements taken at Mulligans flat woodland reserve.
Factors;Sites(9),Elements(6),Inifiltration Suctions(3)
Response; Infiltration ml_per_minute, (also have soil bulk density & soil moisture measurements)
After visualisation reconsidered statistical analysis
Block; Infiltration Suction(3)
Factors; Sites(9), Elements(6), Bulk Density, Soil Moisture
Response; Infiltration ml_per_minute
optional caption text
library(tidyverse)## Warning: package 'tidyverse' was built under R version 3.5.3## -- Attaching packages ------------------------------------------------------------------------- tidyverse 1.2.1 --## v ggplot2 3.1.0 v purrr 0.3.1
## v tibble 2.0.1 v dplyr 0.8.0.1
## v tidyr 0.8.3 v stringr 1.4.0
## v readr 1.3.1 v forcats 0.4.0## -- Conflicts ---------------------------------------------------------------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()library(readxl)## Warning: package 'readxl' was built under R version 3.5.3#Import
MFdata <- read_excel("../Data/MulligansFlatInfiltration.xlsx", skip=5)
#Tidy data, restructure, delete or combine columns, change coulmn structure to factors,
MFdata1 <- MFdata[-c(2,4)]
names(MFdata1) <- c("Site_ID", "Element", "Date", "Bulk_Density_1", "BD1_percent_moisture", "Bulk_Density_2", "BD2_percent_moisture", "Average_Bulk_Density", "Infiltration_Rate_potential_minus4cm", "Infiltration_Rate_potential_minus1cm", "Infiltration_Rate_potential_plus1cm")
#str(MFdata1)
MFdata1 <- mutate_at(MFdata1, vars("Site_ID", "Element"), as.factor)
#str(MFdata1)
MFdata1$Average_moisture_percent <- ((MFdata1$BD1_percent_moisture + MFdata1$BD2_percent_moisture)/2)
MFdata2 <- MFdata1[-c(3,4,5,6,7)] #average BD & infiltration
MFdata2a <- gather(MFdata2, key=Infiltration, value = ml_per_minute, c(4,5,6))
MFdata2a$Infiltration <- factor(MFdata2a$Infiltration, levels = c("Infiltration_Rate_potential_plus1cm", "Infiltration_Rate_potential_minus1cm","Infiltration_Rate_potential_minus4cm"))
MFdata2a$ml_per_minute <- replace(MFdata2a$ml_per_minute, MFdata2a$ml_per_minute == 0.00 , 0.000001) #Need to remove zero before log
MFdata2a$log_ml_per_minute <- log(MFdata2a$ml_per_minute)#log infiltration ml_per_minute
str(MFdata2a)## Classes 'tbl_df', 'tbl' and 'data.frame': 108 obs. of 7 variables:
## $ Site_ID : Factor w/ 9 levels "MF11-2-B","MF19A-2B",..: 7 7 7 7 7 8 8 8 4 4 ...
## $ Element : Factor w/ 6 levels "Clump Bot","Clump Top",..: 6 5 4 1 2 6 5 4 6 5 ...
## $ Average_Bulk_Density : num 0.895 1.064 0.861 0.809 0.683 ...
## $ Average_moisture_percent: num 32.5 25.8 30.9 32.6 31.1 ...
## $ Infiltration : Factor w/ 3 levels "Infiltration_Rate_potential_plus1cm",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ ml_per_minute : num 0.647143 0.464615 0.536889 0.000001 0.0604 ...
## $ log_ml_per_minute : num -0.435 -0.767 -0.622 -13.816 -2.807 ...MFdata3 <- MFdata1[-c(3,8)]
MFdata4 <- gather(MFdata3, key=Bulk_Density, value = grams_per_cubic_cm, c(3,5))
MFdata5 <- gather(MFdata4, key=BD_moisture, value = moisture_percent, c(3,4)) #BD, BDmoisture, & infiltration
MFdata6 <- gather(MFdata5, key=Infiltration, value = ml_per_minute, c(3,4,5)) #tidy but not useful for infiltration
#str(MFdata6)
MFdata6$Infiltration <- factor(MFdata6$Infiltration, levels = c("Infiltration_Rate_potential_plus1cm", "Infiltration_Rate_potential_minus1cm","Infiltration_Rate_potential_minus4cm"))
MFdata6$ml_per_minute <- replace(MFdata6$ml_per_minute, MFdata6$ml_per_minute == 0.00 , 0.000001) #Need to remove zero before log
MFdata6$log_ml_per_minute <- log(MFdata6$ml_per_minute)#log infiltration ml_per_minute
str(MFdata6)## Classes 'tbl_df', 'tbl' and 'data.frame': 432 obs. of 10 variables:
## $ Site_ID : Factor w/ 9 levels "MF11-2-B","MF19A-2B",..: 7 7 7 7 7 8 8 8 4 4 ...
## $ Element : Factor w/ 6 levels "Clump Bot","Clump Top",..: 6 5 4 1 2 6 5 4 6 5 ...
## $ Average_moisture_percent: num 32.5 25.8 30.9 32.6 31.1 ...
## $ Bulk_Density : chr "Bulk_Density_1" "Bulk_Density_1" "Bulk_Density_1" "Bulk_Density_1" ...
## $ grams_per_cubic_cm : num 0.982 1.141 0.924 0.921 0.722 ...
## $ BD_moisture : chr "BD1_percent_moisture" "BD1_percent_moisture" "BD1_percent_moisture" "BD1_percent_moisture" ...
## $ moisture_percent : num 27.3 25.3 29.4 31.6 32.7 ...
## $ Infiltration : Factor w/ 3 levels "Infiltration_Rate_potential_plus1cm",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ ml_per_minute : num 0.647143 0.464615 0.536889 0.000001 0.0604 ...
## $ log_ml_per_minute : num -0.435 -0.767 -0.622 -13.816 -2.807 ...What to plot, this is where the journey was long & windy.
The need for infiltration suction as a block, scaterplot shows no obvious trend.
###Could be a variation between sites, Bulk Density & Moisture percentage
Also logged infiltration rate (ml/min), after looking at residual plot from statistics
Tried some geom_smooth, but no straight lines, random
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
Hypothesis for statistcs; Infiltration Suction trested as a block.
Infiltration Rate (ml/min) affected by Bulk Density & moisture %
Which should be seen in Site_ID, & possibly Element.
Needed to Log(ml/min)
#model data
library(lmerTest)## Warning: package 'lmerTest' was built under R version 3.5.3## Loading required package: lme4## Warning: package 'lme4' was built under R version 3.5.3## Loading required package: Matrix##
## Attaching package: 'Matrix'## The following object is masked from 'package:tidyr':
##
## expand##
## Attaching package: 'lmerTest'## The following object is masked from 'package:lme4':
##
## lmer## The following object is masked from 'package:stats':
##
## stepMFlm1 <- lmer(ml_per_minute~Element + (1|Infiltration), data = MFdata2a)
anova(MFlm1)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Element 13307 2661.4 5 100 1.8424 0.1114summary(MFlm1)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: ml_per_minute ~ Element + (1 | Infiltration)
## Data: MFdata2a
##
## REML criterion at convergence: 1054.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.6846 -0.6364 -0.2120 0.3322 3.7187
##
## Random effects:
## Groups Name Variance Std.Dev.
## Infiltration (Intercept) 822 28.67
## Residual 1445 38.01
## Number of obs: 108, groups: Infiltration, 3
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 22.324 20.845 4.548 1.071 0.338
## ElementClump Top 20.246 17.917 100.000 1.130 0.261
## ElementDispersed Logs -6.666 17.917 100.000 -0.372 0.711
## ElementOld Log 17.030 14.629 100.000 1.164 0.247
## ElementOpen -8.070 14.629 100.000 -0.552 0.582
## ElementTree 12.403 14.629 100.000 0.848 0.399
##
## Correlation of Fixed Effects:
## (Intr) ElmnCT ElmnDL ElmnOL ElmntO
## ElmntClmpTp -0.430
## ElmntDsprsL -0.430 0.500
## ElemntOldLg -0.526 0.612 0.612
## ElementOpen -0.526 0.612 0.612 0.750
## ElementTree -0.526 0.612 0.612 0.750 0.750plot(MFlm1)
# no significant diferrence between elements for ml_per_minute
MFlm2 <- lmer(ml_per_minute~Site_ID + (1|Infiltration), data = MFdata2a)
anova(MFlm2)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Site_ID 27524 3440.5 8 97 2.5624 0.01404 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(MFlm2)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: ml_per_minute ~ Site_ID + (1 | Infiltration)
## Data: MFdata2a
##
## REML criterion at convergence: 1022.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.5845 -0.4719 -0.1169 0.3559 4.0968
##
## Random effects:
## Groups Name Variance Std.Dev.
## Infiltration (Intercept) 824.8 28.72
## Residual 1342.7 36.64
## Number of obs: 108, groups: Infiltration, 3
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 53.599 19.091 3.212 2.808 0.06232 .
## Site_IDMF19A-2B -25.183 13.380 97.000 -1.882 0.06282 .
## Site_IDMF22AZ-4A -27.758 15.450 97.000 -1.797 0.07551 .
## Site_IDMF25A-3A -39.478 14.191 97.000 -2.782 0.00650 **
## Site_IDMF27A-1A -33.798 15.450 97.000 -2.188 0.03110 *
## Site_IDMF32/1A -6.258 14.191 97.000 -0.441 0.66024
## Site_IDMF34-4B -15.453 13.380 97.000 -1.155 0.25095
## Site_IDMF37-1A -47.041 15.450 97.000 -3.045 0.00300 **
## Site_IDMF38-1A -45.243 14.191 97.000 -3.188 0.00193 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) S_IDMF1 S_IDMF22 S_IDMF25 S_IDMF27 S_IDMF32 S_IDMF34
## S_IDMF19A-2 -0.350
## S_IDMF22AZ- -0.303 0.433
## S_IDMF25A-3 -0.330 0.471 0.408
## S_IDMF27A-1 -0.303 0.433 0.375 0.408
## S_IDMF32/1A -0.330 0.471 0.408 0.444 0.408
## S_IDMF34-4B -0.350 0.500 0.433 0.471 0.433 0.471
## S_IDMF37-1A -0.303 0.433 0.375 0.408 0.375 0.408 0.433
## S_IDMF38-1A -0.330 0.471 0.408 0.444 0.408 0.444 0.471
## S_IDMF37
## S_IDMF19A-2
## S_IDMF22AZ-
## S_IDMF25A-3
## S_IDMF27A-1
## S_IDMF32/1A
## S_IDMF34-4B
## S_IDMF37-1A
## S_IDMF38-1A 0.408plot(MFlm2)
# significant difference between sites,
#especially at the following Site_ID; MF25A-3A, MF27A-1A, MF37-1A, MF38-1A.
#residual plot shows need for log transformation
MFlm10 <- lmer(log_ml_per_minute~Site_ID + (1|Infiltration), data = MFdata2a)
anova(MFlm10)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Site_ID 103.39 12.924 8 97 2.5465 0.01459 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(MFlm10)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log_ml_per_minute ~ Site_ID + (1 | Infiltration)
## Data: MFdata2a
##
## REML criterion at convergence: 470.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.5386 -0.3716 0.2192 0.5058 1.3507
##
## Random effects:
## Groups Name Variance Std.Dev.
## Infiltration (Intercept) 3.738 1.934
## Residual 5.075 2.253
## Number of obs: 108, groups: Infiltration, 3
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3.6005 1.2588 2.9996 2.860 0.064568 .
## Site_IDMF19A-2B -2.0685 0.8226 97.0000 -2.515 0.013563 *
## Site_IDMF22AZ-4A -2.1489 0.9499 97.0000 -2.262 0.025911 *
## Site_IDMF25A-3A -1.7540 0.8725 97.0000 -2.010 0.047179 *
## Site_IDMF27A-1A -2.8437 0.9499 97.0000 -2.994 0.003496 **
## Site_IDMF32/1A -0.6654 0.8725 97.0000 -0.763 0.447504
## Site_IDMF34-4B -2.8965 0.8226 97.0000 -3.521 0.000657 ***
## Site_IDMF37-1A -2.6958 0.9499 97.0000 -2.838 0.005528 **
## Site_IDMF38-1A -2.2412 0.8725 97.0000 -2.569 0.011733 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) S_IDMF1 S_IDMF22 S_IDMF25 S_IDMF27 S_IDMF32 S_IDMF34
## S_IDMF19A-2 -0.327
## S_IDMF22AZ- -0.283 0.433
## S_IDMF25A-3 -0.308 0.471 0.408
## S_IDMF27A-1 -0.283 0.433 0.375 0.408
## S_IDMF32/1A -0.308 0.471 0.408 0.444 0.408
## S_IDMF34-4B -0.327 0.500 0.433 0.471 0.433 0.471
## S_IDMF37-1A -0.283 0.433 0.375 0.408 0.375 0.408 0.433
## S_IDMF38-1A -0.308 0.471 0.408 0.444 0.408 0.444 0.471
## S_IDMF37
## S_IDMF19A-2
## S_IDMF22AZ-
## S_IDMF25A-3
## S_IDMF27A-1
## S_IDMF32/1A
## S_IDMF34-4B
## S_IDMF37-1A
## S_IDMF38-1A 0.408plot(MFlm10)
# significant difference between sites,
#especially at the following Site_ID; MF19A-2B, MF22AZ-4A, MF25A-3A, MF27A-1A, MF34-4B, MF37-1A,MF38-1A. MF25A-3A, MF27A-1A, MF37-1A, MF38-1A.
#log_ml_per_minute_ improved residual
MFlm11 <- lmer(log_ml_per_minute~Average_Bulk_Density + (1|Infiltration), data = MFdata2a)
anova(MFlm11)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Average_Bulk_Density 2.3087 2.3087 1 104 0.4046 0.5261summary(MFlm11)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log_ml_per_minute ~ Average_Bulk_Density + (1 | Infiltration)
## Data: MFdata2a
##
## REML criterion at convergence: 497.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.6286 -0.3152 0.0965 0.5613 1.4598
##
## Random effects:
## Groups Name Variance Std.Dev.
## Infiltration (Intercept) 3.721 1.929
## Residual 5.705 2.389
## Number of obs: 108, groups: Infiltration, 3
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.8426 1.8273 12.7221 0.461 0.653
## Average_Bulk_Density 0.7868 1.2369 104.0000 0.636 0.526
##
## Correlation of Fixed Effects:
## (Intr)
## Avrg_Blk_Dn -0.783plot(MFlm11)
# no significant difference between Bulk Density, & Infiltration
# log_ml_per_minute_ improved residual
MFlm12 <- lmer(log_ml_per_minute~Average_moisture_percent + (1|Infiltration), data = MFdata2a)
anova(MFlm12)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Average_moisture_percent 7.0166 7.0166 1 104 1.2396 0.2681summary(MFlm12)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log_ml_per_minute ~ Average_moisture_percent + (1 | Infiltration)
## Data: MFdata2a
##
## REML criterion at convergence: 504.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.8661 -0.3200 0.1924 0.5224 1.3489
##
## Random effects:
## Groups Name Variance Std.Dev.
## Infiltration (Intercept) 3.722 1.929
## Residual 5.660 2.379
## Number of obs: 108, groups: Infiltration, 3
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.98527 1.32963 3.72847 0.741 0.503
## Average_moisture_percent 0.03041 0.02731 104.00000 1.113 0.268
##
## Correlation of Fixed Effects:
## (Intr)
## Avrg_mstr_p -0.518plot(MFlm12)
# no significant difference between Average_moisture_percent
# log_ml_per_minute_ improved residual
MFlm13 <- lmer(log_ml_per_minute~moisture_percent*grams_per_cubic_cm + (1|Infiltration), data = MFdata6)
anova(MFlm13)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value
## moisture_percent 34.134 34.134 1 426 6.3720
## grams_per_cubic_cm 26.285 26.285 1 426 4.9066
## moisture_percent:grams_per_cubic_cm 49.218 49.218 1 426 9.1876
## Pr(>F)
## moisture_percent 0.011956 *
## grams_per_cubic_cm 0.027282 *
## moisture_percent:grams_per_cubic_cm 0.002585 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(MFlm13)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log_ml_per_minute ~ moisture_percent * grams_per_cubic_cm + (1 |
## Infiltration)
## Data: MFdata6
##
## REML criterion at convergence: 1968.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.2406 -0.2960 0.1203 0.5430 1.5597
##
## Random effects:
## Groups Name Variance Std.Dev.
## Infiltration (Intercept) 3.842 1.960
## Residual 5.357 2.315
## Number of obs: 432, groups: Infiltration, 3
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 5.98013 2.64674 53.76706 2.259
## moisture_percent -0.21129 0.08370 426.00000 -2.524
## grams_per_cubic_cm -4.34277 1.96054 425.99999 -2.215
## moisture_percent:grams_per_cubic_cm 0.21474 0.07085 426.00000 3.031
## Pr(>|t|)
## (Intercept) 0.02793 *
## moisture_percent 0.01196 *
## grams_per_cubic_cm 0.02728 *
## moisture_percent:grams_per_cubic_cm 0.00259 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) mstr_p grm___
## mostr_prcnt -0.865
## grms_pr_cb_ -0.894 0.958
## mstr_pr:___ 0.839 -0.987 -0.952plot(MFlm13)
# significant difference between moisture_percent, grams_per_cubic_cm, & moisture_percent*grams_per_cubic_cm
MFlm14 <- lmer(log_ml_per_minute~Average_moisture_percent*Average_Bulk_Density + (1|Infiltration), data = MFdata2a)
anova(MFlm14)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF
## Average_moisture_percent 13.444 13.444 1 102
## Average_Bulk_Density 10.451 10.451 1 102
## Average_moisture_percent:Average_Bulk_Density 17.965 17.965 1 102
## F value Pr(>F)
## Average_moisture_percent 2.4387 0.1215
## Average_Bulk_Density 1.8957 0.1716
## Average_moisture_percent:Average_Bulk_Density 3.2587 0.0740 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(MFlm14)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## log_ml_per_minute ~ Average_moisture_percent * Average_Bulk_Density +
## (1 | Infiltration)
## Data: MFdata2a
##
## REML criterion at convergence: 499.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.9764 -0.2726 0.0948 0.5030 1.4587
##
## Random effects:
## Groups Name Variance Std.Dev.
## Infiltration (Intercept) 3.726 1.930
## Residual 5.513 2.348
## Number of obs: 108, groups: Infiltration, 3
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 8.3509 5.8203 102.0585
## Average_moisture_percent -0.3185 0.2039 102.0000
## Average_Bulk_Density -6.4445 4.6806 102.0000
## Average_moisture_percent:Average_Bulk_Density 0.3116 0.1726 102.0000
## t value Pr(>|t|)
## (Intercept) 1.435 0.154
## Average_moisture_percent -1.562 0.121
## Average_Bulk_Density -1.377 0.172
## Average_moisture_percent:Average_Bulk_Density 1.805 0.074 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) Avrg__ Av_B_D
## Avrg_mstr_p -0.945
## Avrg_Blk_Dn -0.973 0.965
## Avr__:A_B_D 0.920 -0.989 -0.958plot(MFlm14)
# no significant difference between moisture_percent, grams_per_cubic_cm, & moisture_percent*grams_per_cubic_cm
MFlm15 <- lmer(log_ml_per_minute~Site_ID*Element + (1|Infiltration), data = MFdata6)## fixed-effect model matrix is rank deficient so dropping 18 columns / coefficientsanova(MFlm15)## Missing cells for: Site_IDMF22AZ-4A:ElementClump Bot, Site_IDMF25A-3A:ElementClump Bot, Site_IDMF27A-1A:ElementClump Bot, Site_IDMF32/1A:ElementClump Bot, Site_IDMF37-1A:ElementClump Bot, Site_IDMF38-1A:ElementClump Bot, Site_IDMF22AZ-4A:ElementClump Top, Site_IDMF25A-3A:ElementClump Top, Site_IDMF27A-1A:ElementClump Top, Site_IDMF32/1A:ElementClump Top, Site_IDMF37-1A:ElementClump Top, Site_IDMF38-1A:ElementClump Top, Site_IDMF11-2-B:ElementDispersed Logs, Site_IDMF19A-2B:ElementDispersed Logs, Site_IDMF22AZ-4A:ElementDispersed Logs, Site_IDMF27A-1A:ElementDispersed Logs, Site_IDMF34-4B:ElementDispersed Logs, Site_IDMF37-1A:ElementDispersed Logs.
## Interpret type III hypotheses with care.## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Site_ID 469.87 58.733 8 394 15.6514 < 2.2e-16 ***
## Element 124.22 24.845 5 394 6.6207 6.201e-06 ***
## Site_ID:Element 366.41 16.655 22 394 4.4382 4.346e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(MFlm15)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log_ml_per_minute ~ Site_ID * Element + (1 | Infiltration)
## Data: MFdata6
##
## REML criterion at convergence: 1747
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.9044 -0.3964 -0.0038 0.4240 2.8978
##
## Random effects:
## Groups Name Variance Std.Dev.
## Infiltration (Intercept) 3.853 1.963
## Residual 3.753 1.937
## Number of obs: 432, groups: Infiltration, 3
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 3.33153 1.26379 3.05014
## Site_IDMF19A-2B -2.15776 0.79084 394.00000
## Site_IDMF22AZ-4A -1.80066 0.79084 394.00000
## Site_IDMF25A-3A -1.10312 0.79084 394.00000
## Site_IDMF27A-1A -1.23904 0.79084 394.00000
## Site_IDMF32/1A -1.66241 0.79084 394.00000
## Site_IDMF34-4B -6.18787 0.79084 394.00000
## Site_IDMF37-1A -3.45990 0.79084 394.00000
## Site_IDMF38-1A -2.79824 0.79084 394.00000
## ElementClump Top 0.16726 0.79084 394.00000
## ElementDispersed Logs 1.01908 1.11842 394.00000
## ElementOld Log 0.74246 0.79084 394.00000
## ElementOpen -0.15926 0.79084 394.00000
## ElementTree 0.59460 0.79084 394.00000
## Site_IDMF19A-2B:ElementClump Top -0.28419 1.11842 394.00000
## Site_IDMF34-4B:ElementClump Top 2.56717 1.11842 394.00000
## Site_IDMF25A-3A:ElementDispersed Logs -1.77252 1.11842 394.00000
## Site_IDMF32/1A:ElementDispersed Logs 0.39638 1.11842 394.00000
## Site_IDMF19A-2B:ElementOld Log -0.07907 1.11842 394.00000
## Site_IDMF22AZ-4A:ElementOld Log -0.77378 1.11842 394.00000
## Site_IDMF25A-3A:ElementOld Log -1.64256 1.11842 394.00000
## Site_IDMF27A-1A:ElementOld Log -4.99035 1.11842 394.00000
## Site_IDMF32/1A:ElementOld Log 1.18253 1.11842 394.00000
## Site_IDMF34-4B:ElementOld Log 4.58430 1.11842 394.00000
## Site_IDMF37-1A:ElementOld Log 1.27044 1.11842 394.00000
## Site_IDMF38-1A:ElementOld Log 0.83449 1.11842 394.00000
## Site_IDMF19A-2B:ElementOpen 1.30830 1.11842 394.00000
## Site_IDMF22AZ-4A:ElementOpen -0.64158 1.11842 394.00000
## Site_IDMF25A-3A:ElementOpen -0.30919 1.11842 394.00000
## Site_IDMF27A-1A:ElementOpen -0.19427 1.11842 394.00000
## Site_IDMF32/1A:ElementOpen 1.28811 1.11842 394.00000
## Site_IDMF34-4B:ElementOpen 5.33559 1.11842 394.00000
## Site_IDMF37-1A:ElementOpen 0.65119 1.11842 394.00000
## Site_IDMF38-1A:ElementOpen 0.27286 1.11842 394.00000
## Site_IDMF19A-2B:ElementTree -0.49875 1.11842 394.00000
## Site_IDMF34-4B:ElementTree 3.96999 1.11842 394.00000
## t value Pr(>|t|)
## (Intercept) 2.636 0.076575 .
## Site_IDMF19A-2B -2.728 0.006649 **
## Site_IDMF22AZ-4A -2.277 0.023328 *
## Site_IDMF25A-3A -1.395 0.163842
## Site_IDMF27A-1A -1.567 0.117979
## Site_IDMF32/1A -2.102 0.036181 *
## Site_IDMF34-4B -7.824 4.74e-14 ***
## Site_IDMF37-1A -4.375 1.56e-05 ***
## Site_IDMF38-1A -3.538 0.000451 ***
## ElementClump Top 0.211 0.832608
## ElementDispersed Logs 0.911 0.362760
## ElementOld Log 0.939 0.348395
## ElementOpen -0.201 0.840502
## ElementTree 0.752 0.452584
## Site_IDMF19A-2B:ElementClump Top -0.254 0.799554
## Site_IDMF34-4B:ElementClump Top 2.295 0.022237 *
## Site_IDMF25A-3A:ElementDispersed Logs -1.585 0.113805
## Site_IDMF32/1A:ElementDispersed Logs 0.354 0.723219
## Site_IDMF19A-2B:ElementOld Log -0.071 0.943671
## Site_IDMF22AZ-4A:ElementOld Log -0.692 0.489437
## Site_IDMF25A-3A:ElementOld Log -1.469 0.142727
## Site_IDMF27A-1A:ElementOld Log -4.462 1.06e-05 ***
## Site_IDMF32/1A:ElementOld Log 1.057 0.291011
## Site_IDMF34-4B:ElementOld Log 4.099 5.04e-05 ***
## Site_IDMF37-1A:ElementOld Log 1.136 0.256680
## Site_IDMF38-1A:ElementOld Log 0.746 0.456031
## Site_IDMF19A-2B:ElementOpen 1.170 0.242798
## Site_IDMF22AZ-4A:ElementOpen -0.574 0.566533
## Site_IDMF25A-3A:ElementOpen -0.276 0.782346
## Site_IDMF27A-1A:ElementOpen -0.174 0.862188
## Site_IDMF32/1A:ElementOpen 1.152 0.250132
## Site_IDMF34-4B:ElementOpen 4.771 2.59e-06 ***
## Site_IDMF37-1A:ElementOpen 0.582 0.560738
## Site_IDMF38-1A:ElementOpen 0.244 0.807384
## Site_IDMF19A-2B:ElementTree -0.446 0.655887
## Site_IDMF34-4B:ElementTree 3.550 0.000432 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## Correlation matrix not shown by default, as p = 36 > 12.
## Use print(x, correlation=TRUE) or
## vcov(x) if you need it## fit warnings:
## fixed-effect model matrix is rank deficient so dropping 18 columns / coefficientsplot(MFlm15)
#fixed-effect model matrix is rank deficient so dropping 18 columns / coefficients
# significant difference between Site_ID, Element, Site_ID*Element
# especially Site_IDMF19A-2B,Site_IDMF22AZ-4A,Site_IDMF32/1A,Site_IDMF34-4B,Site_IDMF37-1A, Site_IDMF38-1A, Site_IDMF34-4B:ElementClump Top, Site_IDMF27A-1A:ElementOld Log, Site_IDMF34-4B:ElementOld Log, Site_IDMF34-4B:ElementOpen, Site_IDMF34-4B:ElementTree
MFlm16 <- lmer(log_ml_per_minute~Site_ID*Element + (1|Infiltration), data = MFdata2a)## fixed-effect model matrix is rank deficient so dropping 18 columns / coefficientsanova(MFlm16)## Missing cells for: Site_IDMF22AZ-4A:ElementClump Bot, Site_IDMF25A-3A:ElementClump Bot, Site_IDMF27A-1A:ElementClump Bot, Site_IDMF32/1A:ElementClump Bot, Site_IDMF37-1A:ElementClump Bot, Site_IDMF38-1A:ElementClump Bot, Site_IDMF22AZ-4A:ElementClump Top, Site_IDMF25A-3A:ElementClump Top, Site_IDMF27A-1A:ElementClump Top, Site_IDMF32/1A:ElementClump Top, Site_IDMF37-1A:ElementClump Top, Site_IDMF38-1A:ElementClump Top, Site_IDMF11-2-B:ElementDispersed Logs, Site_IDMF19A-2B:ElementDispersed Logs, Site_IDMF22AZ-4A:ElementDispersed Logs, Site_IDMF27A-1A:ElementDispersed Logs, Site_IDMF34-4B:ElementDispersed Logs, Site_IDMF37-1A:ElementDispersed Logs.
## Interpret type III hypotheses with care.## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Site_ID 117.467 14.6834 8 70 2.7807 0.009904 **
## Element 31.056 6.2112 5 70 1.1763 0.329608
## Site_ID:Element 91.602 4.1637 22 70 0.7885 0.728528
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(MFlm16)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log_ml_per_minute ~ Site_ID * Element + (1 | Infiltration)
## Data: MFdata2a
##
## REML criterion at convergence: 370.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.1639 -0.3276 0.0022 0.3657 2.4654
##
## Random effects:
## Groups Name Variance Std.Dev.
## Infiltration (Intercept) 3.733 1.932
## Residual 5.280 2.298
## Number of obs: 108, groups: Infiltration, 3
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 3.33153 1.73332 10.28127 1.922
## Site_IDMF19A-2B -2.15776 1.87624 70.00000 -1.150
## Site_IDMF22AZ-4A -1.80066 1.87624 70.00000 -0.960
## Site_IDMF25A-3A -1.10312 1.87624 70.00000 -0.588
## Site_IDMF27A-1A -1.23904 1.87624 70.00000 -0.660
## Site_IDMF32/1A -1.66241 1.87624 70.00000 -0.886
## Site_IDMF34-4B -6.18787 1.87624 70.00000 -3.298
## Site_IDMF37-1A -3.45990 1.87624 70.00000 -1.844
## Site_IDMF38-1A -2.79824 1.87624 70.00000 -1.491
## ElementClump Top 0.16726 1.87624 70.00000 0.089
## ElementDispersed Logs 1.01908 2.65341 70.00000 0.384
## ElementOld Log 0.74246 1.87624 70.00000 0.396
## ElementOpen -0.15926 1.87624 70.00000 -0.085
## ElementTree 0.59460 1.87624 70.00000 0.317
## Site_IDMF19A-2B:ElementClump Top -0.28419 2.65341 70.00000 -0.107
## Site_IDMF34-4B:ElementClump Top 2.56717 2.65341 70.00000 0.968
## Site_IDMF25A-3A:ElementDispersed Logs -1.77252 2.65341 70.00000 -0.668
## Site_IDMF32/1A:ElementDispersed Logs 0.39638 2.65341 70.00000 0.149
## Site_IDMF19A-2B:ElementOld Log -0.07907 2.65341 70.00000 -0.030
## Site_IDMF22AZ-4A:ElementOld Log -0.77378 2.65341 70.00000 -0.292
## Site_IDMF25A-3A:ElementOld Log -1.64256 2.65341 70.00000 -0.619
## Site_IDMF27A-1A:ElementOld Log -4.99035 2.65341 70.00000 -1.881
## Site_IDMF32/1A:ElementOld Log 1.18253 2.65341 70.00000 0.446
## Site_IDMF34-4B:ElementOld Log 4.58430 2.65341 70.00000 1.728
## Site_IDMF37-1A:ElementOld Log 1.27044 2.65341 70.00000 0.479
## Site_IDMF38-1A:ElementOld Log 0.83449 2.65341 70.00000 0.314
## Site_IDMF19A-2B:ElementOpen 1.30830 2.65341 70.00000 0.493
## Site_IDMF22AZ-4A:ElementOpen -0.64158 2.65341 70.00000 -0.242
## Site_IDMF25A-3A:ElementOpen -0.30919 2.65341 70.00000 -0.117
## Site_IDMF27A-1A:ElementOpen -0.19427 2.65341 70.00000 -0.073
## Site_IDMF32/1A:ElementOpen 1.28811 2.65341 70.00000 0.485
## Site_IDMF34-4B:ElementOpen 5.33559 2.65341 70.00000 2.011
## Site_IDMF37-1A:ElementOpen 0.65119 2.65341 70.00000 0.245
## Site_IDMF38-1A:ElementOpen 0.27286 2.65341 70.00000 0.103
## Site_IDMF19A-2B:ElementTree -0.49875 2.65341 70.00000 -0.188
## Site_IDMF34-4B:ElementTree 3.96999 2.65341 70.00000 1.496
## Pr(>|t|)
## (Intercept) 0.08273 .
## Site_IDMF19A-2B 0.25404
## Site_IDMF22AZ-4A 0.34050
## Site_IDMF25A-3A 0.55846
## Site_IDMF27A-1A 0.51117
## Site_IDMF32/1A 0.37863
## Site_IDMF34-4B 0.00153 **
## Site_IDMF37-1A 0.06941 .
## Site_IDMF38-1A 0.14035
## ElementClump Top 0.92922
## ElementDispersed Logs 0.70210
## ElementOld Log 0.69352
## ElementOpen 0.93260
## ElementTree 0.75225
## Site_IDMF19A-2B:ElementClump Top 0.91501
## Site_IDMF34-4B:ElementClump Top 0.33662
## Site_IDMF25A-3A:ElementDispersed Logs 0.50632
## Site_IDMF32/1A:ElementDispersed Logs 0.88168
## Site_IDMF19A-2B:ElementOld Log 0.97631
## Site_IDMF22AZ-4A:ElementOld Log 0.77144
## Site_IDMF25A-3A:ElementOld Log 0.53790
## Site_IDMF27A-1A:ElementOld Log 0.06417 .
## Site_IDMF32/1A:ElementOld Log 0.65721
## Site_IDMF34-4B:ElementOld Log 0.08845 .
## Site_IDMF37-1A:ElementOld Log 0.63358
## Site_IDMF38-1A:ElementOld Log 0.75408
## Site_IDMF19A-2B:ElementOpen 0.62351
## Site_IDMF22AZ-4A:ElementOpen 0.80965
## Site_IDMF25A-3A:ElementOpen 0.90757
## Site_IDMF27A-1A:ElementOpen 0.94184
## Site_IDMF32/1A:ElementOpen 0.62887
## Site_IDMF34-4B:ElementOpen 0.04819 *
## Site_IDMF37-1A:ElementOpen 0.80685
## Site_IDMF38-1A:ElementOpen 0.91839
## Site_IDMF19A-2B:ElementTree 0.85145
## Site_IDMF34-4B:ElementTree 0.13910
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## Correlation matrix not shown by default, as p = 36 > 12.
## Use print(x, correlation=TRUE) or
## vcov(x) if you need it## fit warnings:
## fixed-effect model matrix is rank deficient so dropping 18 columns / coefficientsplot(MFlm16)
# fixed-effect model matrix is rank deficient so dropping 18 columns / coefficients
# significant difference between Site_ID,
# especially Site_IDMF34-4B, Site_IDMF34-4B:ElementOpen